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A scalable dual-primal domain decomposition method. (English) Zbl 1051.65119

The paper introduces a new method belonging to the class of FETI (finite element tearing and interconnecting) domain decomposition methods for solving second and fourth order boundary value problems discretized by finite elements. The new method is called dual-primal (FETI-DP) as its derivation uses not only dual variables (Lagrange multipliers) for enforcing the interdomain continuity but also primal variables (degrees of freedom corresponding to selected ‘corner’ nodes) enforcing exact continuity in the selected nodes. The new method is advantageous in the use of smaller coarse grid problem in comparison with other FETI methods as well as in higher robustness due to use of non-singular subdomain problems. The reduced coarse grid problem is important for obtaining good parallel scalability for very large number (thousands) of processors.
The paper contains numerical examples showing scalability of the new method with respect to the mesh and subdomain sizes and number of elements per subdomain. The presented examples show also very good parallel scalability obtained on an Origin 2000 system and ASCI Option Red supercomputer.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y05 Parallel numerical computation
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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